Problem: In Takahashi's mind, there is always an integer sequence of length 2 \times 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9}) and an integer P.

Initially, all the elements in the sequence A in Takahashi's mind are 0, and the value of the integer P is 0.

When Takahashi eats symbols `+`, `-`, `>` and `<`, the sequence A and the integer P will change as follows:

* When he eats `+`, the value of A_P increases by 1;
* When he eats `-`, the value of A_P decreases by 1;
* When he eats `>`, the value of P increases by 1;
* When he eats `<`, the value of P decreases by 1.



Takahashi has a string S of length N. Each character in S is one of the symbols `+`, `-`, `>` and `<`. He chose a pair of integers (i, j) such that 1 \leq i \leq j \leq N and ate the symbols that are the i-th, (i+1)-th, ..., j-th characters in S, in this order. We heard that, after he finished eating, the sequence A became the same as if he had eaten all the symbols in S from first to last. How many such possible pairs (i, j) are there?

Constraints

* 1 \leq N \leq 250000
* |S| = N
* Each character in S is `+`, `-`, `>` or `<`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the answer.

Examples

Input

5
+>+<-


Output

3


Input

5
+>+-<


Output

5


Input

48
-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><<


Output

475

Solution (in CPP):

Solution:
#include <map>
#include <string>
#include <vector>
#include <iostream>
using namespace std;
typedef unsigned long long ull;
const ull verse = 259;
const ull inverse = 213668850274628011;
int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	int n; string s;
	cin >> n >> s;
	vector<ull> pw(2 * n + 1); pw[n] = 1;
	for (int i = n + 1; i <= 2 * n; ++i) pw[i] = verse * pw[i - 1];
	for (int i = n - 1; i >= 0; --i) pw[i] = inverse * pw[i + 1];
	vector<ull> hs(n + 1);
	vector<int> dep(n + 1);
	for (int i = 0; i < n; ++i) {
		dep[i + 1] = dep[i];
		if (s[i] == '>') ++dep[i + 1];
		if (s[i] == '<') --dep[i + 1];
		hs[i + 1] = hs[i];
		if (s[i] == '+') hs[i + 1] += pw[n + dep[i + 1]];
		if (s[i] == '-') hs[i + 1] -= pw[n + dep[i + 1]];
	}
	map<ull, int> cnt;
	long long ret = 0;
	for (int i = n; i >= 0; --i) {
		ull tar = hs[n] * pw[n + dep[i]] + hs[i];
		ret += cnt[tar];
		++cnt[hs[i]];
	}
	cout << ret << '\n';
	return 0;
}